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  • 1
    Electronic Resource
    Electronic Resource
    On the boundary value problem of the biharmonic operator on domains with angular corners (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 556-581 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper is concerned with boundary singularities of weak solutions of boundary value problems governed by the biharmonic operator. The presence of angular corner points or points at which the type of boundary condition changes in general causes local singularities in the solution. For that case the general theory of V. A. Kondrat'ev provides a priori estimates in weighted Sobolev norms and asymptotic singular representations for the solution which essentially depend on the zeros of certain transcendental functions. The distribution of these zeros will be analysed in detail for the biharmonic operator under several boundary conditions. This leads to sharp a priori estimates in weighted Sobolev norms where the weight function is characterized by the inner angle of the boundary corner. Such estimates for “negative” Sobolev norms are used to analyse also weakly nonlinear perturbations of the biharmonic operator as, for instance, the von Kármán model in plate bending theory and the stream function formulation of the steady state Navier-Stokes problem. It turns out that here the structure of the corner singularities is essentially the same as in the corresponding linear problem.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020416
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Simple nonconforming quadrilateral Stokes element (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 8 (1992), S. 97-111 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A simple nonconforming quadrilateral Stokes element based on “rotated” multi-linear shape functions is analyzed. On strongly nonuniform meshes the usual parametric version of this element suffers from a lack of consistency, while its nonparametric counterpart turns out to be convergent with optimal orders. This theoretical result is confirmed by numerical tests.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690080202
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    Paper (German National Licenses)
    Fulltext
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